This code triggers sending the "New User Notification" email notification. Example 1 - after the profile update. Example 2 - after create an account during checkout (WooCommerce).

um_send_registration_notification_after_updating_profile.php

<?php

// Send the "New User Notification" email when profile is updated.
add_action( 'um_user_after_updating_profile', function( $to_update, $user_id, $args ) {

	$GLOBALS['um_temp_submitted'] = isset( $args['submitted'] ) ? $args['submitted'] : $args;
	function um_user_after_updating_profile_submitted( $value ) {
		return $GLOBALS['um_temp_submitted'];
	}
	function um_user_after_updating_profile_timestamp( $value ) {
		return time();
	}

	add_filter( 'um_profile_submitted__filter', 'um_user_after_updating_profile_submitted' );
	add_filter( 'um_profile_timestamp_empty__filter', 'um_user_after_updating_profile_timestamp' );
	um_send_registration_notification( $user_id );
	remove_filter( 'um_profile_submitted__filter', 'um_user_after_updating_profile_submitted' );
	remove_filter( 'um_profile_timestamp_empty__filter', 'um_user_after_updating_profile_timestamp' );

}, 20, 3 );

um_send_registration_notification_woocommerce.php

<?php

// Send the "New User Notification" email when a new user is registered via WooCommerce.
add_action( 'woocommerce_created_customer', function( $customer_id, $new_customer_data, $password_generated ) {
	if ( function_exists( 'um_send_registration_notification' ) ) {

		add_filter( 'um_email_send_message_content', function( $message, $slug, $args ) {
			if ( 'notification_new_user' === $slug ) {
				$search  = '{submitted_registration}';
				$replace = '<p>Registered via WooCommerce. See "New order" email for details.</p>';
				$message = str_replace( $search, $replace, $message );
			}
			return $message;
		}, 10, 3 );

		um_send_registration_notification( $customer_id );
	}
}, 10, 3 );